Answer:
- Base Length of 68cm
- Height of 34 cm.
Step-by-step explanation:
Given a box with a square base and an open top which must have a volume of 157216 cubic centimetre. We want to minimize the amount of material used.
Step 1:
Let the side length of the base =x
Let the height of the box =h
Since the box has a square base
Volume 
Surface Area of the box = Base Area + Area of 4 sides
Step 2: Find the derivative of A(x)
Step 3: Set A'(x)=0 and solve for x
![A'(x)=\dfrac{2x^3-628864}{x^2}=0\\2x^3-628864=0\\2x^3=628864\\x^3=314432\\x=\sqrt[3]{314432}\\ x=68](https://tex.z-dn.net/?f=A%27%28x%29%3D%5Cdfrac%7B2x%5E3-628864%7D%7Bx%5E2%7D%3D0%5C%5C2x%5E3-628864%3D0%5C%5C2x%5E3%3D628864%5C%5Cx%5E3%3D314432%5C%5Cx%3D%5Csqrt%5B3%5D%7B314432%7D%5C%5C%20x%3D68)
Step 4: Verify that x=68 is a minimum value
We use the second derivative test
Since the second derivative is positive at x=68, then it is a minimum point.
Recall:
Therefore, the dimensions that minimizes the box surface area are:
- Base Length of 68cm
- Height of 34 cm.
Answer:
D
Step-by-step explanation:
For the first 3 digits the possibilities are
10*9*8 since there is no repeating
The last two letters possiblities are
26*25
10*9*8*26*25 = 468,000
Answer:
41 or 47
Explanation:
First, list all the prime numbers from 40 to 60.
They are 41, 43, 47, 53 and 59.
It says the difference between each digit is 3, so we have to subtract the smaller digit from the larger digit in our list of prime numbers above.
4-1=3
4-3=1
7-4=3
5-3=2
9-5=4
Both 41 and 47 have a difference of 3 between their digits. So your answer is 41 or 47.
Hope this helped you!
Answer:
correct value of x = 5
Step-by-step explanation:
For the baseball camp, you would be paying $18.75 per day. For the basketball camp, you would be paying $20 per day. Judging by the prices, you would be more likely to have a better price for the baseball camp by 1.25. Yes, it isn't that much, but it's still worth it. Hope it helped!
